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Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, az are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. Similarly, the graph of the equation: a₁x² + a₂x² = a₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or

Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, az are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. Similarly, the graph of the equation: a₁x² + a₂x² = a₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Conic Sections
Section: Chapter Questions
Problem 5CC
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Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, a₂ are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. a Similarly, the graph of the equation: α₁x² + ₂x² = α₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or whether the center can be anywhere in the plane), and (iii) the general orientation of the shape (i.e. whether it is aligned along one axis or the other, or whether it is rotated). a. α₁x² = a₁ ao b. a₁x² = a₁ C. a₁x1x₂ = ao d. a₁x² + ₂x₁ = a e. a₁x² + a₂x₂ = ao:
Transcribed Image Text:Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, a₂ are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. a Similarly, the graph of the equation: α₁x² + ₂x² = α₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or whether the center can be anywhere in the plane), and (iii) the general orientation of the shape (i.e. whether it is aligned along one axis or the other, or whether it is rotated). a. α₁x² = a₁ ao b. a₁x² = a₁ C. a₁x1x₂ = ao d. a₁x² + ₂x₁ = a e. a₁x² + a₂x₂ = ao:
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